Chapter Problems 439 9.78 Jurors and gender A jury list contains the names of all in- dividuals who may be called for jury duty. The proportion of the available jurors on the list who are women is 0.53. If 40 people are selected to serve as candidates to serve on the jury, show all steps of a significance test of the hypoth- esis that the selections are random with respect to gender. Set up notation and hypotheses and specify assumptions. а. Five of the 40 selected were women. Find the test b. statistic. Report the P-value and interpret. c. Explain how to make a decision using a significance level of 0.01 d. Refer to the previous exercise. Type I and Type II errors .79 Explain what Type I and Type II errors mean in the context of that exercise. a. b. If you made an error with the decision in part d, is it a Type I or a Type II error?

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.